Speaker: Jin Wei

Abstract: Earlier this year, Bauer and Hanson uploaded a paper to arXiv showing that the reals are countable. Although the submission date, April 1st, is intended for a joke, the paper is entirely serious and highly intriguing. Their result involves constructing an elementary topos within which there exists a surjection from the natural numbers to the Dedekind reals. In this talk, I will give an accessible and friendly introduction to their result. First, I will explain how topos theory plays a role in this context and why this result does not contradict Cantor’s diagonalization proof. Without diving into too much technical details, we will cover the basics of realizability topos and see how their construction creates such “forbidden” surjection. Along the way, we will discover beautiful connections between different areas in math, including constructive analysis, computability theory, and category theory . No prior knowledge is necessary for this talk and everyone is welcome!